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Sunday, January 22, 2012

A real thought experiment that shows virtually nothing

Two weeks ago, we discussed Hannah and Eppley's thought experiment. Hannah and Eppley argued that a fundamental theory that is only partly quantized leads to contradictions either with quantum mechanics or special relativity; in particular we cannot leave gravity unquantized.

However, we also discussed that this thought experiment might be impossible to perform in our universe, since it requires a basically noiseless system and detectors more massive than we have mass available. Unless you believe in a multiverse that offers such an environment - somewhere -, this leaves us in a philosophical conundrum, since we conclude that any contradiction in Hannah and Eppley's thought experiment is unobservable, at least for us. And if you do believe in a multiverse, maybe gravity is only quantized in parts of it.

So you might not be convinced and insist that gravity may remain classical. Here I want to examine this option in more detail and explain why it is not a fruitful approach. If you know a thing or two about semi-classical gravity, you can skip the preliminaries.

Preliminaries

If gravity remained classical, we would have a theory that couples a quantum field to classical general relativity (GR). GR describes the curvature of space-time (denoted R with indices) that is caused by distributions of matter and energy, encoded in the so-called "stress-energy-tensor" (denoted T with indices). The coupling constant is Newton's constant G.

In a quantum field theory, the stress-energy-tensor becomes an operator that acts on elements of the Hilbert-space. But in the equations of GR, one can't just replace the classical stress-energy-tensor with a quantum operator, since the latter has non-vanishing commutators that the former doesn't have. Since both would have to be equal to a tensor-valued function of the classical background, this will not work. Instead, we have to take the classical part of the operator that is it's expectation value, in some quantum state, denoted as usual by the bra-ketsThis is called semi-classical gravity; quantum fields coupled to a classical background. Why, you might ask, don't we just settle for this?

To begin with, semi-classical gravity doesn't actually solve the problems that we were expecting quantum gravity would solve. In particular, semi-classical gravity is the origin rather than the solution of the black-hole information loss problem. It also doesn't prevent singularities (though in some cases it might help). But, you might argue, maybe we were just expecting too much. Maybe the answers to these problems lie entirely elsewhere. That semi-classical gravity doesn't help us here doesn't mean the theory isn't viable, it just means it doesn't do what we wanted it to do. This explains a certain lack of motivation for studying this option, but isn't a good scientific reason to exclude it.

Okay, you have a point here. But semi-classical gravity doesn't only not solve any problems, it brings with it a bunch of new problems. To begin with, the expectation value of the stress-energy-tensor is divergent and has to be regularized, a problem that becomes considerably more difficult in curved space. This is a technical problem which has been studied for some decades now, and that actually with great success. While some problems remain, you might take the point of view that they will be addressed sooner or later.

But a much more severe problem with the semi-classical equations is the measurement process. If you recall, the expectation value of a field that is in a superposition of states that are with probability 1/2 here, and with probability 1/2 there, has to be updated upon measurement. Suddenly then, the particle and its expectation value are with probability 1 here or there. This process violates local conservation of the expectation value of the stress-energy-tensor. But this local conservation is built into GR: It is necessarily always identically fulfilled. This means that semi-classical gravity can't be valid during the measurement. But still, you might insist, we haven't understood the measurement in quantum mechanics anyway, and maybe the theory has to be modified suitably during measurement, so that in fact the conservation law can be temporarily violated.

You are really stubborn, aren't you?

So you insist, but I hope the latter problem illuminated just how absurd semi-classical gravity is if you think about a quantum state in a superposition of different positions, eg a photon that went through a beam splitter. Quantum mechanically, it had 50% chance to go this or that way. But according to semi-classical gravity, its gravitational field went half both ways! If the photon went left, its gravitational field went half with the photon, and half to the right. Surely, you'd think there must be some way to experimentally exclude this absurdity?

Page and Geilker's experiment

Page and Geilker set out in 1981 to show exactly that, the absurdity of semi-classical gravity with a suitably designed experiment. The most amazing thing about their study is that it got published in PRL, for the experiment is absurd in itself.

Their reasoning was as follows. Consider you have a Cavendish-like setup, consisting of two pairs of massive balls connected by rods, see image below (you are looking at the setup from above)The one rod (grey) hangs on a wire that has a mirror attached to it, so you can measure its motion by tracking the position of a laser light shining onto the mirror. The other rod (not shown) connecting the two other balls (blue) will be turned to bring the balls into one of two positions A or B. The gravitational attraction between the balls will cause the wire to twist into one of two directions, as indicated by the arrows.

Or so you think if you know classical gravity. But if the blue balls are in a quantum superposition of A and B, then the gravitational attraction of the expectation value of their mass distribution on the grey balls cancels, the wire doesn't twist, and the laser light doesn't move.

To bring the grey balls into a superposition, Page and Geilker used a radioactive sample that decayed with some probability within 30 seconds, and about with equal probability within a longer time-span after this. Depending on the outcome of the decay, the blue balls remain in position A or assume B. The mirror moved, they concluded the gravitational field of the balls can't have been the expectation value of the superpositions A and B, thus semi-classical gravity is wrong.

Well, I hope you saw Schrödinger's cat laughing. While the decay of a radioactive sample is a purely quantum mechanical process, the wavefunction is long decohered by the time the rod has been adjusted. The blue balls have no more been in a quantum superposition than Schrödinger's cat ever was in a superposition of dead and alive.

This begs the question then if not Page and Geilker's experiment can be realized de facto. The problem is, as always with quantum gravity, that the gravitational interaction is very weak. The heaviest masses that can be brought into a superposition of different locations, presently molecules with some thousand GeV, still have gravitational fields far too weak to be measurable. More can be said about this, but that deserves another post another time.Bottomline

Semi-classical gravity is not considered a fundamentally meaningful description of Nature for theoretical reasons. These are good and convincing reasons, yet semi-classical gravity has stubbornly refused experimental falsification. This tells you just how frustrating the search for quantum gravity phenomenology can be.

52 comments:

I must congratulate you on a most well conceived and therein thought provoking post; one particularly deserving of wide circulation within the science oriented blogosphere. Now I’ll return to having it thought about and listening to my neurons fry.

Thank you for your comment. I believe this is the first time you are posting here, so it seems necessary to point out that we have comment rules, and I do not appreciate self-advertisement. The links to your own papers are only vaguely related to the topic of this post, this is not a post about singularity avoidance. I will leave this comment standing since you are new, but please don't repeat this. Best,

Thanks for the kind words. I find Paul and Geilker's experiment a story that is as amusing as interesting. I wish I knew what was the origin of that investigation. I suspect it was some sort of reply to a challenge somebody else had raised. Best,

Hi Bee,I'm probably being naive, and it wouldn't be the first time, but isn't there a conceptual approach to this problem that may solve some of these problems. I'm not at all saying that I have a mathematical solution that would suit the professional physicists.

First, and i know you know this, the expectation value of a particle's position or momentum is not a particle's actual position or momentum but just its probability. Presumably quantum mechanics is required because the particle's center of mass energy is very small. This is separate from energy density which can still be high. To me it seems that the energy of the actual or virtual photons exchanged with this quantum particle in the detector of the measuring device will overwhelm the particles energy and put the particle in it's final unitary state. To me, that is what Planck's constant is saying: Below a certain center of mass energy the act of detecting a particle's state will be influenced by the exchange of photons used in detecting that state.

On the other hand, above that center of mass energy level the particle, or body, has enough energy, and thus inertia, that you can measure its state reliably without changing it's previous state appreciably. This would be the classical regime. Merging the math between these two regimes is another thing entirely. But I don't think that you can just say that classical statistical gravity is unsatisfactory because the math is unsatisfactory. In the bulk gravity seems to just be tied to the average position, momentum, etc of the object one is measuring. As you say, experiments prove this over and over again that there is a real dividing line between these two regimes in the real world.

But of course it can be a somewhat vague line depending on how you prepare the experiment. If you are using a thermonuclear device to provide the photon exchange with the object you are very likwave better suited to the wave function collapse paradigm, no matter how large the object being measured is.

The transition between the classical and quantum regime doesn't a priori have anything to do with the mass of the object. It just so happens that all elementary particles are very light compared to the Planck scale, meaning that heavy particles have many constituents, thus many degrees of freedom, and thus decohere faster, making quantum effects difficult if not impossible to observe. That having been said, the distinction between classical and quantum by mass only is one that works in practice but not in theory. There is "in principle" nothing that would forbid you to put two particles with masses 10 tons into a superposition and run into exactly the effect that Page and Geilker were looking for. Yet in practice, there are no elementary particles with masses of 10 tons each. Best,

Something is wrong here. I first read about this experiment in Kiefer's book 'Quantum Gravity'(with Unruh's interpratation). There it is described differently (decoherence is not involved). Actually I found it quite good. I don't understand this version though.

I don't know what version you talk about. I was just summarizing the paper. Well, yes, the point is that decoherence is not involved, but it should be when you are talking about objects the mass of a kg. Best,

Thanks for the link. I had not known about Kiefer's summary of the Page and Geilker experiment. It is much better and more truthful to the original paper than my simplification, and would have saved me a lot of time. It is also much better than Page and Geilker's description itself.

However, there are two things to be said. Page and Geilker in their paper are concerned with the many worlds interpretation because they don't want to consider that Tmunu is not covariantly conserved. I have instead swallowed the non-conservation during measurement and stayed with the standard interpretation. As you may have noticed, I am not a friend of the many worlds interpretation. I apologize for abusing their argument in this way.

If, and that is the second point, the experiment actually showed what it was supposed to do. The decoherence I am referring to is that in the transfer of the quantum state from the radioactive decay to the two macroscopic states, so that they actually ever evolve into a superposition for which the classical and semi-classical prediction would differ. I don't really see where this is being addressed? Best,

"The decoherence I am referring to is that in the transfer of the quantum state from the radioactive decay to the two macroscopic states, so that they actually ever evolve into a superposition for which the classical and semi-classical prediction would differ"

Bee my understanding is that they don't have to do that because they use the Everett interpretation. Kiefer says it clearly:

"If the gravitational field were to quantized, one would expect that **each** component of the superposition in |Ψ> would act as a source for the gravitational field. This is of course the Everett interpretation of Quantum theory;"

Bee,I think we are talking around each other on this. I actually agree with Giotis as far as what is being shown in this experiment and disagree with you. But I disagree with Giotis on his interpretation of the experiment's results - verification of MWI - and (more or less) agree with you.

My view is that the experiment showed (classic?) quantum mechanical degeneration between bipolar states but occurring on macroscopic objects. My argument is that the Planck constant only defines the lowest energy parameters in which particles must be described quantum mechanically. It does not describe the maximum size in which objects can be treated that way. What I think defines the maximum size is the amount of energy being used to measure the state of the object.

People normally don't think of measuring a building by blowing it up with dynamite but essentially that is the equivalent of what this experiment is describing in terms of energy levels with radioactive decay. You would then have a binary state of the building both before and after the explosion.That makes a lot more sense to me than MWI. Decoherence not required.

I have to disagree with both of you because I think we don't disagree.

Let us first entangle the issues at hand. There's the experiment. And there is what we can learn (or not learn) from its result. I think we more or less agree on what the experiment was. Then there's the question what we can learn from that. As I already said above, Page and Geilker interpret their experiment in the MWI. They argue that in the MWI the result is incompatible with semi-classical gravity. I haven't gone with their interpretation because I'm not fond of many worlds. In the usual interpretation, the result they find is hardly surprising because, for the reasons I explained above, you wouldn't expect any difference between the classical and the semi-classical result, respectively, in cases where you expect a difference, it's too small to be measureable. In that case you then have to come up with some other way to falsify semi-classical gravity, which is also what Kiefer goes on to explain, and what I was aiming at in my post.

That having been said, it remains surprising to me that the result should differ so greatly between two different interpretations. Giotis, maybe you can illuminate that aspect? Best,

Bee in the MWI each component of the superposition acts as a source for the *quntized* gravitational field i.e. if the gravitational field is quantized. Now the measurement device would react very differently for the two components. So after decoherence one component is picked and thus we would have an instantaneous response by the measurement device.

In the semiclassical case on the other hand by taking the expectation value you are averaging between all the components of the state and thus you would have a much more gentle (not instantaneous) response.

In the wave collapse scheme you would have the same experimental result with the MWI but then you haven't really proved anything because the gravitational field could remain classical. So by eliminating the wave collapse option (by the conservation law not due to the experiment) you are left with only one option MWI.

This is the way I understand the experiment which I found to be very good; you on the other hand for some reason you found it ridiculous:-)

Kiefer seems to be referring to an interpretation by Unruh, which I however don't know. In any case, while the details apparently slightly differ, it is the same experiment in spirit. In both cases there are macroscopic masses supposedly in a superposition state so that the expectation value of the stress-energy differs from that in any one state separately.

I am not sure though I follow your explanation on the many world's interpretation. Why does one average over states that are not coherent? It seems to me there is some implicit assumption here that because the gravitational field is not quantized, there are not 'many' versions of it. I don't see however why this has to be the case. You can have many versions of classical fields, corresponding to different classical solutions. What you cannot have if the field is classical are interferences between them. Best,

I haven’t interjected with a deBroglie-Bohm interpretation of this since as of yet it has never been completely reconciled to being representative of field theory; and then not certain how meaningful one would be. However what I can say is from this perspective there never are any superpositions of a particle as the pilot wave determines the (one) place where a particle goes and always positioned in relation to any particular experimental set up, as the wave has this to be determined. In this case if gravity is left to be classical there will be only one gravitational field to be concerned with respective of any experimental set up and therein after any recorded result.

However one thing this has me mindful of when it comes to Schrodinger type experiments Hawking has said that when he is reminded of the cat he is tempted to get out his gun; and with this example regarding its disputed implications I’m not surprised by such a sentiment:-)

I have trouble deciphering what exactly you want to say. Could you be more explicit?

Anyway here is again what I think it could be a response according to my understanding.

In the case where the gravitational field is quantized you don't average over anything because you don't want to find any expectation value. The state of the quantized gravitational field 'follows' the state of the masses. After decoherence the different *components* of the quantum states are entangled according to MWI. We have two different/separate branches and the component of the quantized gravitational field responds to the component with which it is entangled.

If there is a wave function collapse on the other hand (if you consider it despite the fact that it violates the conservation law) there is no much to say. The wave function of the masses just collapsed and the *classical* gravitational field responded to the collapsed state.

The experimental result is the same but with MWI you have a quantized gravitational field while in the wave function collapse the gravitational field remains classical.

Hmmmm............The Binary Pulsar PSR 1913+16 as a pulse repetition frequency does allow us to say indeed that such events in the cosmos do allow information to be transmitted back to us as a picture of their closing distances. So, the frequency increases?

What message is really being sent then if we cannot say the connection to this event is not linked by "some method" that allows gravitational waves to be produced?

You look at the earth as a massive particle and there are ways in which we are mapping the gravitational field, the moon as well, so we are definitively seeing the universe in a way that is consistent as well as very aptly describing the constituent as some larger particle?

Perhaps GR cannot be quantized because it is selectively wrong. Einstein-Cartan vacuum background active only upon fermionic mass need only be testable. It is believable afterward. Quantize empirically complete gravitation.

I understand the fundamental differences between QM and GR and hence the search for quantum gravity. However, another motivation is the successful unification of other forces (electricity with magnetism, electroweak unification etc) where there were really no fundamental differences but the resulting theory is more economical (i.e. Maxwell's equations explain a lot with just a little). However, there seems to be a feeling that all forces must be unified as a matter of principle. Is there any reason to believe this? From this point of view (though perhaps not from the point of view of fundamental differences), it could be that gravity is something fundamentally different than other forces.

Another point: the RSS feeds for most blogs say "comment on by , rather than the first few lines of the comment, as is the case here. I find the former much more useful. Anyway to change it?

Philip,I agree about gravity being different from the other forces. My previous argument about using higher energy to facilitate probing of gravitational objects was used mostly because of my priorities. I hate the MWI interpretation in qm. One must use what is needed to defeat the enemy, mwi.

My personal opinion about gravity is that it is much more akin to what we normally describe in atmospheric terms. The unseen vacuum energy is that atmosphere. It is a finite amount of energy that never changes. When objects wrap up more energy during acceleration it reduces the pressure of this energy atmosphere surrounding the object. This creates a low pressure area around the object resulting the effects that are observed. This would cause not only time dilation around objects of high.energy, but would also imply a speed up of time in the early universe when the vacuum energy was more dense. Of course it would require that most physicists give up the free lunch of multiverses, mwi, and the science fiction that there is more energy now than what we started with.

Bee, I'm not necessarily lumping you in with most physicists because you seem to have a more open mind than most!

My question is basically why should I in the MWI, for states that have decohered, use the above semi-classical equation averaged over all states, and not a classical gravitational field coupled to just the expectation value in the branch I'm sitting in, which would give the proper classical behavior. Best,

You write "there seems to be a feeling that all forces must be unified as a matter of principle." I don't have this impression, it depends on where you look. String theory aims at the unification of all forces, all right, and the hope is that the additional requirement gives you additional hints for how to do it correctly. Loop quantum gravity otoh doesn't aim at any such unification. They probably wouldn't mind, but it's not on the agenda. The same can be said for other approaches to quantum gravity like causal dynamical triangulation, causal sets, what else is there... emergent gravity approaches often add some dummy matter (scalar fields, non-descript non-chiral fermions, etc), so they don't seem to think the matter content is crucial. Asymptotically safe gravity is somewhat on the borderline in the sense that it unifies all and everything in a common framework, yet that's not all people like to associate with unification, so it depends on how you define it. Best,

Now you are both misrepresenting and misunderstanding me. I didn't say the experiment is silly, I said it is absurd. It is absurd because I doubt anybody had expected a different outcome, yet somebody had to go and do it publish it. My question was not how do you compute an expectation value in MWI. My questions was why should I in the MWI use the semi-classical equation rather than coupling each decohered part to its own classical metric. I can't do that in the normal interpretation because it doesn't make any sense, I'd end up with a family of classical metrics. But it makes sense in the MWI. Best,

"My questions was why should I in the MWI use the semi-classical equation rather than coupling each decohered part to its own classical metric."

Because the rules of QM forbids you to do that. Since the wave function has not collapsed you must take the expectation value for the whole wave function if you want to treat the QM part quantum mechanically.

The strong point is not that they use MWI as a precondition but that they have excluded the wave function collapse interpretation due to incompatibility with the semiclassical theory (due to conservation law).

PS

Absurd and silly are quite close but anyway sorry if I have misrepresented you.

It's interesting to look back at earlier thoughts on this subject. For example, back in 1962 Feynman made some comments that can be found starting on page 11 of "Feynman's Lectures on Gravitation". He wrote "The extreme weakness of quantum gravitational effects now poses some philosophical problems; maybe nature is trying to tell us something new here, maybe we should not try to quantize gravity... Is it possible that gravity is not quantized and all the rest of the world is? There are some arguments that have been made in the past that the world cannot be one-half quantum and one-half classical..." He then described one such argument (already "old" in 1962) involving the gravitational waves emitted by an electron in a two-slit experiment.

After concluding that this thought experiments seems to imply gravity must be quantized, he hedged a bit, saying "In spite of these arguments we would like to keep an open mind. It is still possible that quantum theory does not absolutely guarantee that gravity MUST be quantized... [for example,] if there were some mechanism by which the phase evolution for very complex objects had a little bit of smearing in it, so it was not absolutely precise, then our amplitudes would become probabilities [and] there might be some consequences of this smearing. If one such consequence were the existence of gravitation itself, then there would be no quantum theory of gravitation, which would be a terrifying idea for the rest of these lectures." (To be fair, he added that "these are very wild speculations...")

I think if a person as intelligent as Richard Feynman had known back then about the small current measured accelerated expansion of the universe he wouldn't have referred to the non-quantization of gravity as "wild speculation". It changes everything.

I think if a person as intelligent as Richard Feynman had known back then about the small current measured accelerated expansion of the universe he wouldn't have referred to the non-quantization of gravity as "wild speculation". It changes everything.

Philip,I feel I'm already possibly in hot water with Bee over this. But I'll indulge myself and you this once and then shut up. Forgive me Bee.

It seems to me that if gravity was essentially an atmospheric force based on the vacuum energy that it would show up in just this way. Because my math is poor compared to many of you folks I'm sure many will look down on anything I have to say based on that. But i don't think condemning the messenger because of this will make some of these issues go away.

Vacuum energy can be considered proxy for the cosmological constant. Vaccum energy has the effect of pressure and will cause an expansion of the universe. It has always been assumed that this energy adds up in all modes and frequencies right up to the Planck Length frequency per unit volume of space. Of course if this is true according to Einstein's equations it would add up to enormous expansionary acceleration of the universe.

So naturally it was assumed that there is something canceling this out. The total vacuum energy density per unit volume then equals zero. So it was assumed by many, including many here I'm sure, that this settles it. In fact, most people now assume that each volume of space that is added to the universe has a total positive energy of 10^120 more than it should and then justify it by saying either 1. MWI or 2. The multiverse says that energy can be made from nothing and that it isn't conserved, at least not locally in our universe. Beside that, they also pull out of their ass that there must be negative energy that balances that density to zero eventhough there is no experimental evidence for it. Anti matter doesn't exist in sufficient quantities to serve that purpose.

So this whole theoretical structure of the mwi, or multiverse, or negative energy serves the purpose of justifying this erroneous energy density number. But we KNOW now through this acceleration that they don't cancel and the energy density is small and positive.

The most logical explanation to me is that the universe started out with a high vacuum energy density at the beginning, which accounts for the larger structure smoothness due to the high accelerations at the beginning. But now it is low density after the expansion. Vacuum energy is conserved as the universe expands. And that small vacuum energy density is the reason for weakness of gravity. The gravitational force is a byproduct of composite matter's interaction with the vacuum energy.

I think I already overstayed my welcome on this subject. I would have a lot more to say about how that energy serves as an atmospheric component but this is Bee's blog so give me your email if you want further exchange on it.

Yes, you'd need a macroscopic quantum superposition that lasted some time to do the experiment. First hid the B balls behind some screen, have everything supercooled and darkened, and then itstead of the B balls use a bose einstein condensate make to have an center of mass in a superposition. Now the experiment described should essentially work. Either Balls A, won'tknow where to move do, or the gravity alone will collapse the superposition of the position of center of mass.

You haven't understood what the issue is. You need a macroscopic superposition of two position states, please re-read again what I wrote. It doesn't make any difference for the outcome of the experiment what the composition is of B. Best,

@Eric: The blog is not the place for a detailed discussion, but here are a few points:

The cosmological constant corresponds to a negative pressure.

It is also not conserved. Rather, it is constant per volume (which is why it is called the cosmological constant) and so grows with the volume of the universe.

I don't really see a problem with the 120 orders of magnitude which the particle physicists keep talking about. To me, someone that far off with an estimate doesn't deserve to be taken seriously. :-) I realize that many people go for the (almost) cancelling explanation, including Weinberg, who cancels the particle-physics cosmological constant with a negative "pure" cosmological constant which is slightly larger in absolute value, justifying the coincidence with anthropic arguments (though not explicitly invoking the many-worlds interpretation of QM nor the multiverse, IIRC). Personally, I don't see the point in worrying about this until particle physics comes up with a precise and robust prediction.

The observed astronomical cosmological constant is an observational fact. As far as we know, it corresponds exactly to the cosmological constant as introduced by Einstein. Yes, other models have been examined, but there is not one shred of evidence that what we observe is not the classical cosmological constant. There are some astronomers specifically trying to measure its equation of state, which will tell us more. As far as we can tell now, omega is -1, i.e. the traditional cosmological constant. In my view, if it turns out to be anything other than -1, this will be a more important discovery than the acceleration of the universe (which has been a theoretical possibility since the 1920s) and of course more than the expansion of the universe (which is no big deal; it can expand, contract or be static, and the last solution is unstable, so the probability of expansion is 50% - epsilon).

Without further evidence, we shouldn't assume that the particle-physics vacuum energy has anything to do with the astronomical cosmological constant.

@Philip"Without further evidence, we shouldn't assume that the particle-physics vacuum energy has anything to do with the astronomical cosmological constant."

I'm not arguing for anything more than consistency. One must use the same level of rigor and judgement to both sides of any argument. In this case most physicists, and also yourself, are not applying the same rigor to physical evidence of many worlds, alternate universes, or the equivalent of negative energy in the form of supersymetry. You are mistaking consensus and politics in physics on your side with physical evidence. In other words, it is very easy to go with flow, which is what you are basically doing. Critical thinking is hard and generally makes enemies so I understand why so many people just go with the consensus and call it fact.

Eric, I don't see what you are accusing me of. While I think some of your ideas are not well founded, I also criticize the establishment in my previous comment and am certainly not going with the flow.

I don't think I have publicly taken a stance on MWI and am sure I have never publicly written anything on supersymmetry. Dave Schramm would have accused me of thinking like an astronomer instead of a physicist (bonus points if you recognize the reference).

In my latest refereed-journal paper (arXiv:1112.1666, accepted by MNRAS), I demonstrate that the flatness problem doesn't exist. That is swimming more or less straight into the flow.

@PhillipSorry for misspelling your name earlier. I used the american spelling and it wasn't intentional.

"It is also not conserved. Rather, it is constant per volume (which is why it is called the cosmological constant) and so grows with the volume of the universe.)"

I'm not sure what you are saying here unless there is a key element I'm missing. I think this is the crux of where we disagree. Wouldn't a constant cosmological constant cause a constant accelerating expansion of the universe? I'm leaving aside the matter of the balance of matter and it's gravitation with it for the moment. How do you get around this?

Actually, both spellings exist on both sides of the pond. Mine is somewhat less common. No problem.

The influence of matter cannot be neglected. A pure cosmological constant results in exponential expansion. This has been known since the 1920s. For a universe described by the Friedmann-Lemaitre equations, this is a straightforward result.

We cannot prove, the gravity is not classical, until we define it classically. The following story illustrates the limits of this approach clearly.

This story begins in dark ages. A group of theorists seeks for violation of gravitational law at short distances. They indeed find nothing, because their wooden experimental device is not sensitive enough. OK...The sensitivity of devices improves gradually, until some experimentalist finds the solely unexpected electrostatic force, which no gravity theory considered so far...Next generation of theorists already knows about it - so they arrange their experiments in such a way, the electrostatic force doesn't interfere their gravitometric measurements. And again, they find no violation of gravitational law at short distances...The sensitivity of devices improves gradually, until some experimentalist finds the solely unexpected Van DerWaals dipole force, which no gravity theory considered so far.Next generation of theorists already knows about it - so they arrange their experiments in such a way, neither electrostatic force, neither dipole forces interfere their sensitive gravitometric measurements. As usually, they find no violation of gravitational law at short distances...The sensitivity of devices improves gradually, until some experimentalist finds the solely unexpected Casimir force, which no gravity theory considered so far.Next generation of theorists already knows about it - so they arrange their experiments in such a way, neither electrostatic force, neither dipole force, neither Casimir force interferes their extra-sensitive gravitometric measurements. As usually, they find no violation of gravitational law at short distances...The sensitivity of devices improves gradually, until some experimentalist finds the solely unexpected thermal Casimir force, which no gravity theory considered so far.Next generation of theorists already knows about it - so they arrange their experiments with single neutrons in such a way, neither electrostatic force, neither dipole force, neither Casimir force, neither thermal Casimir force (..ffffuuuu...!) interferes their ultra-mega-sensitive gravitometric measurements. As usually, they find no violation of gravitational law at short distances...

What physical theorists are doing in schematic way is actually both a good joke, both school of life for those, who are paying their nonsensical job from their taxes.

Good parable Zephir. My personal feeling is that the universe is economical in it's basic laws. I'll never be dissuaded from it. And given that feeling I will never accept that there is one vacuum energy density for gravity and another for the quantum regime. It doesn't make no sense no how.

Until that is resolved in my opinion there will be no resolution between quantum mechanics and GR. My personal feeling is that just as GR and SR show that their is no special reference place in the universe that you can tell from simple observation, there is also some invariance principle that says you cannot tell what stage of universe expansion you are in from simple observation. We just haven't figured out mathematically what the invariance principle is yet.

I'll add one more somewhat theological premise that I believe in: the universe was created in such a way that we we can figure it out. In other words - the energy of our one universe is conserved. Without that we are lost. It would be almost like a hoax otherwise when we are able to figure so much out locally but have the final questions be unanswerable globally. That is the fatalism most physicists have succumbed to, present host of this blog excepted.

Bee: "Maybe you can tell me how it would solve the problems that I elaborated on in this earlier post, that quantum gravity is supposed to address?"

Well, if we see GR and QM as complementary in the same sense that the waveform and particle are complementary, then, to quote Wittgenstein, the "solution of the problem" would consist in "the vanishing of the problem," no?

In other words, there may be a point beyond which science, in principle, cannot venture. Or, to put it another way: if there is no quantum world, then there is no world in which quantum mechanics and general relativity can co-exist.

And what I'm asking you is not whether you agree, but what sort of problems would be posed by such a position, over and above the sort of problems already revealed by Bohr's interpretation of the aporia of quantum physics.

I apologize, Bee. I hadn't read the post to which you refer in your previous comment, only the newer one. The original post does seem to discuss the sort of problems I was requesting. Let me read it more carefully and think about it. Thanks so much by the way for this GREAT blog, with so many extremely interesting posts on physics, etc.